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MARIA GOEPPERT MAYER
June 2S, 1906-February 20,1972
BY ROBERT G. SACHS
WHEN IN 1963 she received the Nobel Prize in Physics,
Maria Goeppert Mayer was the second woman in history
to win that prize- the first being Marie Curie, who had received
it sixty years earlier�and she was the third woman in history
to receive the Nobel Prize in a science category. This accomplish-
ment had its beginnings in her early exposure to an intense
atmosphere of science, both at home and in the surrounding
university community, a community providing her with the
opportunity to follow her inclinations and to develop her re-
markable talents under the guidance of the great teachers and
scholars of mathematics and physics. Throughout her full and
gracious life, her science continued to be the theme about which
her activities were centered, and it culminated in her major
contribution to the understanding of the structure of the atomic
nucleus, the spin-orbit coupling shell model of nuclei.
Maria Goeppert was born on June 28, 1906, in Kattowiz,
Upper Silesia (then in Germany), the only child of Friedrich
Goeppert and his wife, Maria nee Wolff. In 1910 the family
moved to Gottingen, where Friedrich Goeppert became Pro-
fessor of Pediatrics. Maria spent most of her life there until
marriage.
On January 19, 1930, she married Joseph E. Mayer, a
chemist (elected to the National Academy of Sciences in 1946),
311
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312
BIOGRAPHICAL MEMOIRS
and they had two children: Maria Ann, now Maria Mayer
Wentzel, and Peter Conrad. Maria Goeppert Mayer became a
citizen of the United States in 1933. She died on February 20,
1972.
Both her father's academic status and his location (Gottin-
gen) had a profound influence on her life and career. She was
especially proud of being the seventh straight generation of
university professors on her father's side. Her father's personal
influence on her was great. She is quoted as having said that her
father was more interesting than her mother, "He was after all
a scientist." ~ She was said to have been told by her father that
she should not grow up to be a woman, meaning a housewife,
and therefore decided, "I wasn't going to be just a woman." ~
The move to Gottingen came to dominate the whole struc-
ture of her education, as might be expected. Georgia Augusta
University, better known simply as "Gottingen," was at the
height of its prestige, especially in the fields of mathematics and
physics during the period when she was growing up. She was
surrounded by the great names of mathematics and physics.
David Hilbert was an immediate neighbor and friend of the
family. Max Born came to Gottingen in 1921 and James Franck
followed soon after; both were close friends of the Goeppert
family. Richarc! Courant, Hermann Weyl, Gustav Herglotz,
and Edmund Landau were professors of mathematics.
The presence of these giants of mathematics and physics
naturally attracted the most promising young scholars to the
institution. Through the years, Maria Goeppert came to meet
and know Arthur Holly Compton, Max Delbrueck, Paul A. M.
Dirac, Enrico Fermi, Werner Heisenberg, John van Neumann,
J. Robert Oppenheimer, Wolfgang Pauli, Linus Pauling, Leo
Szilard, Edward Teller, and Victor Weisskopf. It was the oppor-
~ Joan Dash, A fife of One's Own (New York: Harper and Row, 1973), p. 231.
t Ibid.
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MARIA GOEPPERT MAYER
313
tunity to work with James Franck that led to Joseph Mayer's
coming to Gottingen and gave him the chance to meet and
marry her.
Maria Goeppert was attracted to mathematics very early and
planned to prepare for the University, but there was no public
institution in Gottingen serving to prepare girls for this pur-
pose. Therefore, in 1921 she left the public elementary school
to enter the Frauenstudium, a small private school run by suf-
ragettes to prepare those few girls who wanted to seek admission
to the University for the required examination. The school
closed its doors before the full three-year program was com-
pleted, but she decided to take the University entrance exami-
nation promptly in spite of her truncated formal preparation.
She passed the examination and was admitted to the University
in the spring of 1924 as a student of mathematics. Except for
one term spent at Cambridge University, England, her entire
career as a university student was completed at Gottingen.
In 1924 she was invited by Max Born to join his physics
seminar, with the result that her interests started to shift from
mathematics to physics. It was just at this time that the great
developments in quantum mechanics were taking place, with
Gottingen as one of the principal centers; in fact, Gottingen
might have been described as a "cauldron of quantum mechan-
ics" at that time; and in that environment Maria Goeppert was
molded as a physicist.
As a student of Max Born, a theoretical physicist with a
strong foundation in mathematics, she was well trained in the
mathematical concepts required to understand quantum me-
chanics. This and her mathematics education gave her early style
of research a strong mathematical flavor. Yet the influence of
James Franck's nonmathematical approach to physics certainly
became apparent later. In fact, a reading of her thesis reveals
that Franck already had an influence at that stage of her work.
She completed her thesis and received her doctorate in 1930.
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BIOGRAPHICAL MEMOIRS
The thesis was devoted to the theoretical treatment of double
photon processes. It was described many years later by Eugene
Wigner as a "masterpiece of clarity and concreteness." Although
at the time it was written the possibility of comparing its theo-
retical results with those of an experiment seemed remote, if
not impossible, double photon phenomena became a matter of
considerable experimental interest many years later, both in
nuclear physics and in astrophysics. Now, as the result of the
development of lasers and nonlinear optics, these phenomena
are of even greater experimental interest.
After receiving her degree, she married and moved to Balti-
more, Maryland, where her husband, Joseph Mayer, took up an
appointment in the Chemistry Department of Johns Hopkins
University. Opportunities for her to obtain a normal profes-
sional appointment at that time, which was at the height of
the Depression, were extremely limited. Nepotism rules were
particularly stringent then and prevented her from being con-
sidered for a regular appointment at Hopkins; nevertheless,
members of the Physics Department were able to arrange for a
very modest assistantship, which gave her access to the Univer-
sity facilities, provided her with a place to work in the Physics
Building, and encouraged her to participate in the scientific
activities of the University. In the later years of this appoint-
ment, she also had the opportunity to present some lecture
courses for graduate students.
At the time, the attitude in the Physics Department toward
theoretical physics gave it little weight as compared to experi-
mental research; however, the department included one out-
standing theorist, Karl Herzfeld, who carried the burden of
teaching all of the theoretical graduate courses. Herzfeld was
an expert in classical theory, especially kinetic theory and ther-
modynamics, and he had a particular interest in what has come
to be known as chemical physics. This was also Joseph Mayer's
primary field of interest, and under his and Herzfeld's guid-
ance and influence Maria Mayer became actively involved in
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MARIA GOEPPERT MAYER
315
this field, thereby deepening and broadening her knowledge of
physics.
However, she did not limit herself to this one field but took
advantage of the various talents existing in the Johns Hopkins
department, even going so far as to spend a brief period working
with R. W. Wood, the dean of the.Johns Hopkins experimen-
talists. Another member of the department with whom she had
a substantial common interest was Gerhard Dieke. The Mathe-
matics Department, which was quite active at that time, included
Francis Murnaghan and Aurel Wintner, with whom she devel-
oped particularly close connections. However, the two members
of the Johns Hopkins faculty who had the greatest influence
were her husband and Herzfeld. Not only did she write a num-
ber of papers with Herzfeld in her early years there, but also
they became close, lifelong friends.
The rapid development of quantum mechanics was having
a profound effect in the field of chemical physics in which she
had become involved, and the resulting richness and breadth
of theoretical chemical physics was so great as to appear to have
no bounds. She was in a particularly good position to take
advantage of this situation, since no one at Johns Hopkins had
a background in quantum mechanics comparable to hers. In
particular, she became involved in pioneering work on the
structure of organic compounds with a student of Herzfeld's,
Alfred Sklar; and in that work she applied her special mathe-
matical background, using the methods of group theory and
. . .
matrix mechanics.
During the early years in Baltimore, she spent the summers
of 1931, 1932, and 1933 back in Gottingen, where she worked
with her former teacher, Max Born. In the first of those sum-
mers she completed with him their article in the Handbuch der
Physik, "Dynamische Gittertheorie der Kristalle." In 1935 she
published her important paper on double beta-decay, repre-
senting a direct application of techniques she had used for her
thesis, but in an entirely different context.
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BIOGRAPHICAL MEMOIRS
Later, James Franck joined the faculty at Johns Hopkins
and renewed his close personal relationship with the Mayers.
Also in that later period, Edward Teller became a member of
the faculty of George Washington University, in nearby Wash-
ington, D.C., and she looked to him for guidance in the devel-
oping frontiers of theoretical physics. At about the same time,
she became deeply involved in a collaboration with Joseph
Mayer in writing the book Statistical Mechanics, published
in 1940.
When as her first bona fide student I turned to her for guid-
ance in choosing a research problem, nuclear physics was on
the rise; and she told me that that was the only field worth con-
sideration by a beginning theorist. She took me to Teller to ask
his advice about possible research problems. Our resulting joint
work was her first publication in the field of nuclear physics.
My thesis problem on nuclear magnetic moments was also se-
lected with Teller's help, and she gave her guidance throughout
that work, suggesting application to this problem in nuclear
physics of techniques of quantum mechanics in which she was
so proficient. These two forays into the field were her only
activities in the physics of nuclear structure until after World
WarII.
Her approach to quantum mechanics, having been so greatly
influenced by Born, gave preference to matrix mechanics over
Schroedinger wave mechanics. She was very quick with matrix
manipulations and the use of symmetry arguments to obtain
answers to a specific problem, and this ability stood her in good
stead in her later work on nuclear shell structure, which led to
her Nobel Prize. She appeared to think of physical theories, in
general, and quantum mechanics, in particular, as tools for
solving physics problems and was not much concerned with the
philosophical aspects or the structure of the theory.
When she had the opportunity to teach graduate courses,
her lectures were well organized, very technical, and highly con-
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MARIA GOEPPERT MAYER
317
densed. She spent little time on background matters or physical
interpretation. Her facility with the methods of theoretical
physics was overwhelming to most of the graduate students, in
whom she inspired a considerable amount of awe. At the same
time, the students took a rather romantic view of this young
scientific couple, known as " Joe and Maria," and felt that it was
a great loss when they left Johns Hopkins to go to Columbia
University in 1939.
At Columbia University, where Joseph Mayer had been
appointed to an associate professorship in chemistry, Maria
Mayer's position at first was even more tenuous than at Johns
Hopkins. The chairman of the Physics Department, George
Pegram, arranged for an office for her, but she had no appoint-
ment.
This was the beginning of a close relationship between the
Mayers and the Harold Ureys, a relationship which was to con-
tinue throughout her life, as they always seemed to turn up in the
same places in later years. Willard Libby became a good friend,
and it was at Columbia that she first began to come under the
influence of Enrico Fermi, although she had already met him in
her first summer in the United States (1930) at the University of
Michigan Special Summer Session in Physics. The Mayers also
saw much of I. I. Rabi and Jerrold Zacharias during their years
at Columbia.
She quickly put to work her talent for problem solving when
Fermi suggested that she attempt to predict the valence-shell
structure of the yet-to-be-discovered transuranium elements. By
making use of the very simple Fermi-Thomas model of the
electronic structure of the atom, she came to the conclusion that
these elements would form a new chemical rare-earth series. In
spite of the oversimplifications of the particular model, this
subsequently turned out to be a remarkably accurate prediction
of their qualitative chemical behavior.
In December 1941, she was offered her first real position: a
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BIOGRAPHICAL MEMOIRS
half-time job teaching science at Sarah Lawrence College, and
she organized and presented a unified science course, which was
developed as she went along during that first presentation. She
continued, on an occasional basis, to teach part time at Sarah
Lawrence throughout the war.
She was offered a second job opportunity in the spring of
1942 by Harold Urey, who was building up a research group
devoted to separating U 235 from natural uranium as part of
the work toward the atomic bomb. This ultimately became
known as Columbia University's Substitute Alloy Materials
(SAM) Project. She accepted this second half-time job, which
gave her an opportunity to use her knowledge of chemical
physics. Her work included research on the thermodynamic
properties of uranium hexafluoride and on the theory of sepa-
rating isotopes by photochemical reactions, a process that, how-
ever, did not develop into a practical possibility at that time.
(The much later invention of the laser has reopened that possi-
bility.)
Edward Teller arranged for her to participate in a program
at Columbia referred to as the Opacity Project, which concerned
the properties of matter and radiation at extremely high tem-
peratures and had a bearing on the development of the thermo-
nuclear weapon. Later, in the spring of 1945, she was invited to
spend some months at Los Alamos, where she had the oppor-
tunity to work closely with Teller, whom she considered to be
one of the world's most stimulating collaborators.
In February of 1946, the Mayers moved to Chicago where
Joe had been appointed Professor in both the Chemistry De-
partment and the newly formed Institute for Nuclear Studies
of The University of Chicago. At the time, the University's
nepotism rules did not permit the hiring of both husband and
wife in faculty positions, but Maria became a voluntary Associ-
ate Professor of Physics in the Institute, a position which gave
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MARIA GOEPPERT MAYER
319
her the opportunity to participate fully in activities at the
University.
Teller hail also accepted an appointment at The University
of Chicago, and he moved the Opacity Project there, giving
Maria Mayer the opportunity to continue with this work. It
was accommodated in the postwar residuum of the Metallurgi-
cal Laboratory of the University where, in its heyday during
the war, the initial work on the nuclear chain reaction had been
carried out. She was hired as a consultant to the Metallurgical
Laboratory so that she could continue her participation in this
project, and several students from Columbia who hack become
graduate students at Chicago worked under her guidance.
The Metallurgical Laboratory went out of existence to make
way for establishing Argonne National Laboratory on July 1,
1946, under the aegis of the newly formed Atomic Energy Com-
mission. She was offered and was pleased to accept a regular
appointment as Senior Physicist (half time) in the Theoretical
Physics Division of the newly formed laboratory. The main
interest at Argonne was nuclear physics, a field in which she
had had little experience, and so she gladly accepted the oppor-
tunity to learn what she could about the subject. She continued
to hold this part-time appointment throughout her years in
Chicago, while maintaining her voluntary appointment at the
University. The Argonne appointment was the source of finan-
cial support for her work during this very productive period of
her life, a period in which she made her major contribution
to the field of nuclear physics, the nuclear shell model, which
earned her the Nobel Prize.
Since the mission of Argonne National Laboratory at the
time was, in addition to research in basic science, the develop-
ment of peaceful uses of nuclear power, she also became in-
volved in applied work there. She was the first person to under-
take the solution by electronic computer of the criticality prob-
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BIOGRAPHICAL MEMOIRS
lem for a liquid metal breeder reactor. She programmed this
calculation (using the Monte Carlo method) for ENIAC, the first
electronic computer, which was located at the Ballistic Research
Laboratory, Aberdeen Proving Ground. A summary of this
work was published in 1951 (U.S. Department of Commerce,
Applied Mathematics, Series 12: 19-20~.
While carrying on her work at Argonne, she continued her
voluntary role at The University of Chicago by lecturing to
classes, serving on committees, directing thesis students, and
participating in the activities at the Institute for Nuclear Studies
(now known as the Enrico Fermi Institute). The University had
pulled together in this Institute a stellar assembly of physicists
and chemists, including Fermi, Urey, and Libby, as well as
Teller and the Mayers. Gregor Wentzel joined the faculties of
the Physics Department and Institute later, and the families
quickly became very close, one outcome being the joining of
the families by marriage of Maria Ann to the Wentzels' son.
Subrahmanyan Chandrasekhar, who had beers on the faculty
of the Astronomy Department for many years, also joined the
Institute. A stream of young and very bright physical scientists
poured into the Institute, and the atmosphere was stimulating
to the extreme. To add to this exciting atmosphere, which in
some ways must have been reminiscent of Gottingen in the early
days, her former teacher and friend, James Franck, was already
a member of the University's Chemistry Department.
The activities in the Institute reflected the interests of the
leading lights, interests that were very broad indeed, ranging
from nuclear physics and chemistry to astrophysics and from
cosmology to geophysics. The interdisciplinary character of the
Institute was well suited to the breadth of her own activities
over the past, so that her Chicago years were the culmination
of her variety of scientific experience. In keeping with this, she
turned her attention at first to completing and publishing some
earlier work in chemical physics, including work with Jacob
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MARIA GOEPPERT MAYER
321
Bigeleisen on isotopic exchange reactions. Bigeleisen had col-
laborated with her in other work at Columbia University and at
this time was a fellow of the Institute. At the same time, she
began to give attention to nuclear physics.
Among the many subjects being discussed at the Institute
was the question of the origin of the chemical elements. Teller
was particularly interested in this subject and induced Maria
Mayer to work with him on a cosmological model of the origin
of the elements. In pursuit of data required to test any such
model, she became involved in analyzing the abundance of the
elements and noticed that there were certain regularities associ-
ating the highly abundant elements with specific numbers of
neutrons or protons in their nuclei. She soon learned that Walter
M. Elsasser had made similar observations in 1933, but she had
much more information available to her and found not only
that the evidence was stronger but also that there were addi-
tional examples of the effect. These specific numbers ultimately
came to be referred to as "magic numbers," a term apparently
invented by Eugene Wigner.
When she looked into information other than the abun-
dance of the elements, such as their binding energies, spins, and
magnetic moments, she found more and more evidence that
these magic numbers were in some way very special and came
to the conclusion that they were of great significance for the
understanding of nuclear structure. They suggested the notion
of stable "shells" in nuclei similar to the stable electron shells
associated with atomic structure, but the prevailing wisdom of
the time was that a shell structure in nuclei was most unlikely
because of the short range of nuclear forces as compared to the
long-range coulomb forces holding electrons in atoms. There
was the further difficulty that the magic numbers did not fit
simple-minded ideas associated with the quantum mechanics of
shell structure.
Maria Mayer persisted in checking further evidence for shell
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BIOGRAPHICAL MEMOIRS
structure, such as nuclear beta-decay properties and quadrupole
moments, and in trying to find an explanation in terms of the
quantum mechanics of the nuclear particles. In this she was
greatly encouraged by Fermi and had many discussions with
him. She was also strongly supported by her husband, who acted
as a continual sounding board for her thoughts on the subject
and provided the kind of guidance that could be expected from
a chemist who, in many ways, was better equipped to deal with
phenomena of this kind than a physicist. The systematics of
regularities in behavior with which she was faced had great
similarity to the systematics in chemical behavior that had led to
the classical development of valence theory in chemistry, and
whose fundamental explanation had been found in the Pauli
Exclusion Principle.
It was Fermi who asked her the key question, "Is there any
indication of spin-orbit coupling?" whereupon she immediately
realized that that was the answer she was looking for, and thus
was born the spin-orbit coupling shell model of nuclei.
Her ability to immediately recognize spin-orbit coupling as
the source of the correct numerology was a direct consequence
of her mathematical understanding of quantum mechanics and
especially of her great facility with the numerics of the represen-
tations of the rotation group. This ability to instantly identify
the key numerical relationships was most impressive, and even
Fermi was surprised at how quickly she realized that his aues-
tion was the key to the problems
-
1
While she was preparing the spin-orbit coupling model for
~ Joseph Mayer gives the following description of this episode: "Fermi and
Maria were talking in her office when Enrico was called out of the office to
answer the telephone on a long distance call. At the door he turned and asked
his question about spin-orbit coupling. He returned less than ten minutes later
and Maria started to 'snow' him with the detailed explanation. You may remem-
ber that Maria, when excited, had a rapid fire oral delivery, whereas Enrico
always wanted a slow detailed and methodical explanation. Enrico smiled and
left: 'Tomorrow, when you are less excited, you can explain it to me.'"
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MARIA GOEPPERT MAYER
323
publication she learned of a paper by other physicists presenting
a different attempt at an explanation and, as a courtesy, she
asked the Editor of the Physical Review to hold her brief Letter
to the Editor in order that it appear in the same issue as that
paper. As a result of this delay, her work appeared one issue
following publication of an almost identical interpretation of
the magic numbers by Otto Haxel, J. Hans D. Jensen, and Hans
E. Suess. Jensen, working completely independently in Hei(lel-
berg, had almost simultaneously realized the importance of
spin-orbit coupling for explaining the shell structure, and the
result had been this joint paper.
Maria Mayer and Jensen were not acquainted with one an-
other at the time, and they did not meet until her visit to
Germany in 1950. In 1951 on a second visit, she and Jensen had
the opportunity to start a collaboration on further interpreta-
tion of the spin-orbit coupling shell model, and this was the
beginning of a close friendship as well as a very productive
scientific effort. It culminated in the publication of their book,
Elementary Theory of Nuclear Shell Structure (1955~. They
shared the Nobel Prize in 1963 for their contributions to this
subject.
After Fermi's death in 1954, other members of the Institute
for Nuclear Studies who had provided so much stimulation for
her left Chicago. Teller had gone earlier in 1952, Libby left in
1954, and Urey in 1958. In 1960 she accepted a regular appoint-
ment as Professor of Physics at the University of California at
San Diego when both she and her husband had the opportunity
to go there.
Her appointment as a full professor in her own right at a
major university was very gratifying to her, and she looked
forward to the stimulation of this newest interdisciplinary group
of scientists that was being drawn together there. However,
shortly after arriving in San Diego, she had a stroke, and her
years there were marked by continuing problems with her health.
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BIOGRAPHICAL MEMOIRS
Nevertheless, she continued to teach and to participate actively
in the development and exposition of the shell model. Her last
publication, a review of the shell model written in collaboration
with Jensen, appeared in 1966; and she continued to give as
much attention to physics as she could until her death in
early 1972.
In addition to being elected to the National Academy of
Sciences in 1956 and receiving the Nobel Prize in 1963, Maria
Goeppert Mayer's honors included being elected a Correspond-
ing Member of the Akademieder Wissenschaften in Heidelberg
and receiving honorary degrees of Doctor of Science from Rus-
sell Sage College, Mount Holyoke College, and Smith College.
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MARIA GOEPPERT MAYER
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1929
325
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With K. F. Herzfeld. On the states of aggregation. J. Chem. Phys.,
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1938
With R. G. Sacks. Calculations on a new neutron-proton interaction
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With A. L. Sklar. Calculations of the lower excited levels of benzene.
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1940
With Joseph E. Mayer. Statistical Mechanics. N.Y.: Wiley.
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With K. l. McCallum. Calcuations of the absorption spectrum of
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With Jacob Bigeleisen. Calculation of equilibrium constants for
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1948
With Jacob Bigeleisen, Peter C. Stevenson, and John Turkevich.
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The structure of the nucleus. Scientific American, March.
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With i. H. D. Jensen. Electromagnetic effects due to spin-orbit
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With V. L. Telegdi. Twin neutrino theory. A modified ~ component
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The shell model. Science, 145:999-1006.
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OCR for page 329
Representative terms from entire chapter:
goeppert mayer
